A Continuous DUE Algorithm Using the Link Transmission Model

• Published in: Networks and spatial economics Vol. 15; no. 3; pp. 465 - 483
• Main Authors: Nezamuddin, N., Boyles, Stephen D.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.09.2015; Springer Nature B.V
• Subjects: Algorithms; Bans; Civil Engineering; Control theory; Dynamics; Economic models; Economic statistics; Economic theory; Economics; Economics and Finance; Equilibrium; Links; Mathematical models; Networks; Operations Research/Decision Theory; Regional/Spatial Science; Route choice; Route selection; Routing (telecommunications); Studies; Traffic assignment; Traffic congestion; Traffic control; Traffic flow; Transportation economics; Travel; Vehicles; Newton-based algorithm; Continuous flow model; Link transmission model
• ISSN: 1566-113X; 1572-9427
• DOI: 10.1007/s11067-014-9234-x

This paper describes a continuous-flow, continuous-time model for which a dynamic Wardrop equilibrium provably exists. This formulation is general, but is particularly designed to include the link and node models of Yperman’s Link Transmission Model as a special case. Rather than using path flows to describe route choice, travelers are aggregated by destination and node-specific routing parameters are used to reduce the number of control variables needed. Furthermore, this formulation allows efficient solution methods from static traffic assignment, such as Linear User Cost Equilibrium (LUCE), to be applied in a fairly straightforward manner. Demonstrations on a small network verify the effectiveness of this dynamic LUCE algorithm in our model, showing favorable performance comapred to the method of successive averages.